Question

Given the following transformations 𝑦 = 3𝑓(− 2𝑥 + 8) − 6 to the parent function 𝑓(𝑥) = 𝑙𝑜𝑔(small2)(x), describe (in words) how to determine the following key features of the transformed function without
graphing:

Domain:
Range:
x-Int:
y-int:
Asymptotes:

Please help me.

Answer 1

f(x) = log_2(x)
domain: x > 0
range: all reals
intercepts (1,0)
asymptotes: x=0

3f(-2x+8)=3f(-2(x-4)) is f(x)
shifted right by 4
reflected across the y-axis
compressed horizontally by 2
stretched vertically by 3
So that gives us
domain: (-2x+8) > 0 or x < 4
range: all reals
intercepts -2x+8=1, or (3.5,0) and (0,9)
asymptotes: x=4

see the graph at

https://www.wolframalpha.com/input/?i=3log_2%28-2x%2B8%29

Answer 2

oops. I forgot the downward shift of 6.
You can probably figure out what that affects., with the help of

https://www.wolframalpha.com/input/?i=3log_2%28-2x%2B8%29-6